New approach to scaling rules for stellar and planetary dynamos

TL;DR

This paper develops new scaling rules for magnetic fields and time scales in stellar and planetary dynamos using dimensional analysis and physical arguments, challenging traditional assumptions and providing more accurate relationships.

Contribution

It introduces a novel approach to derive dynamo scaling laws by combining dimensional analysis with physical reasoning and linear instability analysis, moving beyond MAC balance assumptions.

Findings

Derived scaling rules for magnetic field strengths.

Established relationships between external and internal magnetic fields.

Linked differential rotation to dynamo mechanism details.

Abstract

Glorified dimensional analysis is used to derive scaling rules for internal and external magnetic field strengths and various time scales. Naive dimensional analysis is inconclusive because of multiple time scales, but physical arguments serve to weed out irrelevant parameters. Time scales can be derived from linearized instability analysis instead of ill-founded assumptions of Magnetic-Archimedean-Coriolis (MAC) balance. Further relationships can be derived from high-level models of coupled main field components and differential rotation. The ratios of the external dipole field to internal magnetic fields and of differential to overall rotation depend on details of the dynamo mechanism.